A Note on the Optimal Convergence Rate of Descent Methods with Fixed Step Sizes for Smooth Strongly Convex Functions

André Uschmajew () and Bart Vandereycken ()
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André Uschmajew: Max Planck Institute for Mathematics in the Sciences
Bart Vandereycken: University of Geneva

Journal of Optimization Theory and Applications, 2022, vol. 194, issue 1, No 17, 364-373

Abstract: Abstract Based on a result by Taylor et al. (J Optim Theory Appl 178(2):455–476, 2018) on the attainable convergence rate of gradient descent for smooth and strongly convex functions in terms of function values, an elementary convergence analysis for general descent methods with fixed step sizes is presented. It covers general variable metric methods, gradient-related search directions under angle and scaling conditions, as well as inexact gradient methods. In all cases, optimal rates are obtained.

Keywords: Convergence rate estimates; Variable metric method; Inexact gradient method; SR1 update; 90C25; 65K05 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10957-022-02032-z

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